Self-gravitating fluid shells and their non-spherical oscillations in Newtonian 
theory

Bicak, Jiri; Schmidt, Bernd G.

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Self-gravitating fluid shells and their non-spherical oscillations in Newtonian theory

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Bicak, Jiri
AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

Schmidt, Bernd G.
AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Citation

Bicak, J., & Schmidt, B. G. (1999). Self-gravitating fluid shells and their non-spherical oscillations in Newtonian theory. Astrophysical Journal, 521(2), 708-717.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-5882-8

Abstract

We summarize the general formalism describing surface Ñows in three-dimensional space in a form
which is suitable for various astrophysical applications. We then apply the formalism to the analysis of
nonradial perturbations of self-gravitating spherical Ñuid shells. Spherically symmetric gravitating shells
(or bubbles) have been used in numerous model problems especially in general relativity and cosmology.
A radially oscillating shell was recently suggested as a model for a variable cosmic object. Within Newtonian
gravity we show that self-gravitating static Ñuid shells are unstable with respect to linear nonradial
perturbations. Only shells (bubbles) with a negative mass (or with a charge the repulsion of which
is compensated by a tension) are stable.